1) A music store specialises in three types of CDs: classical, blues and heavy metal. In one week they sold a total of 420 CDs. THey sold 10% more classical than blues while sales of heavy metal constituted 50% more than the combined sales of classical and blues CDs. How many of each type of CD did they sell?

2) A is three times as old as B. In three years' time, B will be three times as old as C. In fifteen years' time, A will be three times as old as C. What are their present ages?

3) Henry and Thomas Wong collect basketball cards. Henry has five sixths the number of cards that Thomas has. The Wright family also has a collection of cards. George Wright has half as many cards again as Thomas, Sally Wright has 18 less than Thomas and Zeb Wright has one third the number Thomas has.

i: Write an expression for each child's number of cards in terms of the number Thomas has.

ii: The Wright family owns six more cards than the Wong family. Find the number of cards each child has collected.

So far:

Henry = H
Thomas = T
George = G
Sally = S
Zeb = Z

H = (5/6)T
G = (1/2)T
S = T - 18
Z = (1/3)T

(5/6)T = (1/2)T + T - 18 + (1/3)T + 6
(5/6)T = (11/6) + 6 -18
t = 12

Substituting that into the previous equations for each child should give the correct number of cards, but for Sally (T - 18, 12 - 18 = -6) it returns a negative value and therefore cannot be correct.

Let the age of B = x years ----- 1
Then age of A = 3x years ----- 2
Let the age of C = y years
AFTER 3 YEARS
Age of B = x + 3
Age of C = (y + 3) years
It is given that age of B = 3 times age of C that is:
(x+ 3 ) = 3 ( y+3) OR 3y = x – 6 --- 3
AFTER 15 YEARS
Age of A = 3x + 15
Age of C = y + 15
It is given that Age of A = 3 times Age of C That is
3x + 15 = 3 ( y + 15) = 3y + 45 = ( x-6) + 45 [ using (3) ]
3x + 15 = x – 6 + 45 OR 2x = 24 and thus x = 12
Hence the present age of A = 36 years,
Present age of B = 12 years and the present age of C = 2 years